Ladar Transmitter with Ellipsoidal Reimager

ABSTRACT

Disclosed herein is a compact beam scanner assembly that includes an ellipsoidal reimaging mirror.

CROSS-REFERENCE AND PRIORITY CLAIM TO RELATED PATENT APPLICATIONS

This patent application is a continuation of U.S. patent applicationSer. No. 16/865,687, filed May 4, 2020, and entitled “Ladar Transmitterwith Ellipsoidal Reimager”, now U.S. Pat. No. ______, which is acontinuation of U.S. patent application Ser. No. 16/051,707, filed Aug.1, 2018 and entitled “Ladar Transmitter with Ellipsoidal Reimager”, nowU.S. Pat. No. 10,642,029, which is a continuation of U.S. patentapplication Ser. No. 15/644,242, filed Jul. 7, 2017 and entitled “LadarTransmitter with Optical Field Splitter/Inverter”, now U.S. Pat. No.10,042,159, which is (1) a continuation-in-part of U.S. patentapplication Ser. No. 15/431,065, filed Feb. 13, 2017 and entitled “LadarTransmitter with Optical Field Splitter/Inverter for Improved Gaze onScan Area Portions”, which claims priority to (i) U.S. provisionalpatent application 62/297,126, filed Feb. 18, 2016 and entitled “LadarTransmitter with Resonant Scan Optical Field Splitter/Inverter” and (ii)U.S. provisional patent application 62/439,378, filed Dec. 27, 2016 andentitled “Ladar Transmitter with Improved Gaze on Scan Area Portions”,and (2) a continuation-in-part of U.S. patent application Ser. No.15/431,096, filed Feb. 13, 2017 and entitled “Ladar Transmitter withInduced Phase Drift for Improved Gaze on Scan Area Portions”, whichclaims priority to (i) U.S. provisional patent application 62/297,126,filed Feb. 18, 2016 and entitled “Ladar Transmitter with Resonant ScanOptical Field Splitter/Inverter” and (ii) U.S. provisional patentapplication 62/439,378, filed Dec. 27, 2016 and entitled “LadarTransmitter with Improved Gaze on Scan Area Portions”, the entiredisclosures of each of which are incorporated herein by reference.

INTRODUCTION

It is believed that there are great needs in the art for improvedcomputer vision technology, particularly in an area such as automobilecomputer vision. However, these needs are not limited to the automobilecomputer vision market as the desire for improved computer visiontechnology is ubiquitous across a wide variety of fields, including butnot limited to autonomous platform vision (e.g., autonomous vehicles forair, land (including underground), water (including underwater), andspace, such as autonomous land-based vehicles, autonomous aerialvehicles, etc.), surveillance (e.g., border security, aerial dronemonitoring, etc.), mapping (e.g., mapping of sub-surface tunnels,mapping via aerial drones, etc.), target recognition applications,remote sensing, safety alerting (e.g., for drivers), and the like).

As used herein, the term “ladar” refers to and encompasses any of laserradar, laser detection and ranging, and light detection and ranging(“lidar”). Ladar is a technology widely used in connection with computervision. Ladar systems share the high resolution and intuitive feel ofpassive optic sensors with the depth information (ranging) of a radarsystem. In an exemplary ladar system, a transmitter that includes alaser source transmits a laser output such as a ladar pulse into anearby environment. Then, a ladar receiver will receive a reflection ofthis laser output from an object in the nearby environment, and theladar receiver will process the received reflection to determine adistance to such an object (range information). Based on this rangeinformation, a clearer understanding of the environment's geometry canbe obtained by a host processor wishing to compute things such as pathplanning in obstacle avoidance scenarios, way point determination, etc.However, conventional ladar solutions for computer vision problemssuffer from high cost, large size, large weight, and large powerrequirements as well as large data bandwidth use. The best example ofthis being vehicle autonomy. These complicating factors have largelylimited their effective use to costly applications that require onlyshort ranges of vision, narrow fields-of-view and/or slow revisit rates.

For example, ladar systems are known in the art where a ladartransmitter illuminates a large number of range points simultaneously.Flash ladar is an example of such a system. However, these conventionalsystems are believed to suffer from a number of shortcomings. Forexample, flash ladar systems require a very high energy per pulse laser,which is not only costly but can also be an eye hazard. Furthermore, theread-out integrated circuits for flash ladar systems are typically quitenoisy. Also, the wide field-of-view signal-to-noise ratio (SNR) forflash ladar systems is typically very low, which results in shortranges, thereby detracting from their usefulness.

In an effort to satisfy the needs in the art for improved ladar-basedcomputer vision technology, the inventor has disclosed a number ofembodiments for methods and systems that apply scanning ladartransmission concepts in new and innovative ways, as described in U.S.patent application Ser. No. 62/038,065, filed Aug. 15, 2014 and U.S.Pat. App. Pubs. 2016/0047895, 2016/0047896, 2016/0047897, 2016/0047898,2016/0047899, 2016/0047903, and 2016/0047900, the entire disclosures ofeach of which are incorporated herein by reference.

The inventor believes that there are needs in the art for furtherimprovements on how scanning ladar transmitters can be designed tooptimize their gaze on regions of interest in the environment. Whileradars have been highly optimized with scheduling methods to dwell(gaze) where gaze is needed when gaze is needed, conventional ladarsystems today do not share this dwell optimality. This is because ladarsuffer from the very thing that makes them attractive: their resolution.

This is because, while even the world's largest radars have thousands ofbeam choices upon which to dwell, even a small automotive ladar systemfitting in the palm of the hand routinely has 100,000+ or even millionsof choices for dwell. This leads to two general design choices for ladarengineers: (i) mechanically step from dwell to dwell, or (ii) useresonant mirrors that rapidly scan through the scene. Design approach(i) is precise and adaptable but is extremely slow in environments wherethere are large numbers of interrogation cells present. Design approach(ii) has historically been non-adaptable. To improve upon theseconventional design approaches, the inventors disclose techniques bywhich one can reduce the disadvantages of resonant mirror-based ladarwhile achieving much of the acuity and specificity that historically hasonly been available to mechanical stepping techniques and without losingthe speed advantages of resonant scanning mirrors.

In example embodiments, the inventors disclose designs for a fieldsplitter/inverter that can be used in combination with high speed scanssuch as Lissajous scans to improve the gaze of a ladar transmitter ondesired scan areas (such as a center region of a scan area). Theinventors further disclose how an induced periodic phase drift can beincorporated into a Lissajous scan to further improve gaze by reducingscan gaps in desired regions, while doing so in a manner that can ensurelow amplitude and zero impact on periodicity, thereby ensuring beamquality and preserving mensuration.

In example embodiments, the inventors also disclose a compact beamscanner assembly that includes an ellipsoidal conjugate reflectorreimaging mirror. The ellipsoidal mirror can be positioned opticallybetween first and second scannable mirrors. A lens can be positionedoptically upstream from the first scannable mirror. Such an arrangementcan provide (among other benefits) a compact beam scanner design wherethe two scannable mirrors are equally sized and placed closely togetherwithin the assembly. Moreover, reimaging can be especially useful whenused in combination with field inversion, since it limits the additionalupscope headroom needed for an inverter lens.

These and other features and advantages of the present invention will bedescribed hereinafter to those having ordinary skill in the art.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and B illustrate example embodiments of ladartransmitter/receiver systems.

FIG. 2A depicts an example embodiment of a ladar transmitter.

FIG. 2B shows a scan area defined by two scannable mirrors for anexample scanning ladar transmitter.

FIG. 2C shows a top view of the scan arrangement defined by FIG. 2B.

FIG. 3 shows a beam scanner that includes a field splitter/inverter inaccordance with an example embodiment.

FIG. 4 shows a top view of the beam scanner arrangement defined by FIG.3.

FIG. 5 shows how the field splitter/inverter operates to split andinvert the scan pattern of the mirrors across the scan area.

FIG. 6A shows a perspective view of a field splitter/inverter inaccordance with another example embodiment.

FIGS. 6B and 6C show additional views of the field splitter/inverter ofFIG. 6A.

FIG. 6D shows an example embodiment of a hinged field splitter/inverterthat exhibits an adjustable mirror pitch angle.

FIG. 7 shows an example ray tracing with respect to beam paths in thefield splitter/inverter of FIGS. 6A-C.

FIG. 8 shows an example of how a split/inverted scan area can beoverlapped.

FIG. 9 is a table that exhibits performance results for different usecases of a ladar transmitter.

FIG. 10A depicts an example of a standard Lissajous scan pattern.

FIG. 10B depicts an example of a split/inverted Lissajous scan pattern.

FIG. 10C depicts the revisit performance of the Lissajous scan patternof FIG. 10A.

FIG. 10D depicts a plot of revisit performance for an example of asplit/inverted Lissajous scan revisit when a field inverter is employedto provide inversion along elevation.

FIGS. 11A and B depict where scan gaps exist in connection with the scanpatterns of FIGS. 10A and 10B respectively.

FIG. 12 depicts an example process flow for inducing a periodic phasedrift into a Lissajous scan pattern.

FIGS. 13A and B depict scan gaps projected onto a ground plane forexample use cases of a non-inverted Lissajous scan and an invertedLissajous scan respectively.

FIGS. 14A and 14B show example inverted Lissajous scan patterns withinduced phase drift and no induced phase drift respectively.

FIG. 15 shows an example embodiment of an ellipsoidal conjugatereflector (ECR) reimaging system.

FIG. 16 displays the scanned field for a conventional scanner asconfigured without ray fan aligned reimaging optics.

FIG. 17 displays an embodiment of a reimager with geometry chosen perour disclosed design formula. Note that the ray fan directed downwardfrom the reimager lies in a plane containing the center of the secondscanning mirror.

FIG. 18 displays the elimination of distortions in the scanned outputfield made possible by using an ellipsoidal reflector in a mannerconsistent with an example embodiment.

FIG. 19 is a side-looking schematic of an example embodiment of an ECR2D scanner.

FIG. 20 shows the use of paired “kissing” mirrors as a virtual, lowcost, source of field inversion.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

FIG. 1A illustrates an example embodiment of a ladartransmitter/receiver system 100. The system 100 includes a ladartransmitter 102 and a ladar receiver 104, each in communication withsystem interface and control 106. The ladar transmitter 102 isconfigured to transmit a plurality of ladar pulses 108 toward aplurality of range points 110 (for ease of illustration, a single suchrange point 108 is shown in FIG. 1A). Ladar receiver 104 receives areflection 112 of this ladar pulse from the range point 110. Ladarreceiver 104 is configured to receive and process the reflected ladarpulse 112 to support a determination of range point distance [depth] andintensity information. In addition the receiver 104 determines spatialposition information [in horizontal and vertical orientation relative tothe transmission plane] by any combination of (i) prior knowledge oftransmit pulse timing, and (ii) multiple detectors to determine arrivalangles.

In example embodiments, the ladar transmitter 102 can take the form of aladar transmitter that includes scanning mirrors. Furthermore, in anexample embodiment, the ladar transmitter 102 uses a range point downselection algorithm to support pre-scan compression (which can bereferred herein to as “compressive sensing”), as shown by FIG. 1B. Suchan embodiment may also include an environmental sensing system 120 thatprovides environmental scene data to the ladar transmitter 102 tosupport the range point down selection. Specifically, the controlinstructions will instruct a laser source when to fire, and willinstruct the transmitter mirrors where to point. Example embodiments ofsuch ladar transmitter designs can be found in U.S. patent applicationSer. No. 62/038,065, filed Aug. 15, 2014 and U.S. Pat. App. Pubs.2016/0047895, 2016/0047896, 2016/0047897, 2016/0047898, 2016/0047899,2016/0047903, and 2016/0047900, the entire disclosures of each of whichare incorporated herein by reference. Through the use of pre-scancompression, such a ladar transmitter can better manage bandwidththrough intelligent range point target selection. An example embodimentof ladar receiver 104 can be found in U.S. patent application Ser. No.62/297,126, filed Feb. 18, 2016. While these referenced and incorporatedpatent applications describe example embodiments for the ladartransmitter 102 and ladar receiver 104, it should be understood thatpractitioners may choose to implement the ladar transmitter 102 and/orladar receiver 104 differently than as disclosed in these referenced andincorporated patent applications.

FIG. 2A depicts an example embodiment for a ladar transmitter 104 asdisclosed by the above-referenced and incorporated patent applications.The ladar transmitter 104 can include a laser source 200 in opticalalignment with laser optics 202, a beam scanner 204, and transmissionoptics 206. These components can be housed in a packaging that providesa suitable shape footprint for use in a desired application. Forexample, for embodiments where the laser source 200 is a fiber laser orfiber-coupled laser, the laser optics 202, the beam scanner 204, and anyreceiver components can be housed together in a first packaging thatdoes not include the laser source 200. The laser source 200 can behoused in a second packaging, and a fiber can be used to connect thefirst packaging with the second packaging. Such an arrangement permitsthe first packaging to be smaller and more compact due to the absence ofthe laser source 200. Moreover, because the laser source 200 can bepositioned remotely from the first packaging via the fiber connection,such an arrangement provides a practitioner with greater flexibilityregarding the footprint of the system.

Based on the control information transmitter control instructions, suchas a shot list 212 generated by system control 106, a beam scannercontroller 208 can be configured to control the nature of scanningperformed by the beam scanner 204 as well as control the firing of thelaser source 200. A closed loop feedback system 210 can be employed withrespect to the beam scanner 204 and the beam scanner controller 208 sothat the scan position of the beam scanner 204 can be finely controlled,as explained in the above-referenced and incorporated patentapplications.

The laser source 200 can be any of a number of laser types suitable forladar pulse transmissions as described herein.

For example, the laser source 200 can be a pulsed fiber laser. Thepulsed fiber laser can employ pulse durations of around 1-4 ns, andenergy content of around 0.1-100 μJ/pulse. The repetition rate for thepulsed laser fiber can be in the kHz range (e.g., around 1-500 kHz).Furthermore, the pulsed fiber laser can employ single pulse schemesand/or multi-pulse schemes as described in the above-referenced andincorporated patent applications. However, it should be understood thatother values for these laser characteristics could be used. For example,lower or higher energy pulses might be employed. As another example, therepetition rate could be higher, such as in the 10's of MHz range(although it is expected that such a high repetition rate would requirethe use of a relatively expensive laser source under current marketpricing).

As another example, the laser source 200 can be a pulsed IR diode laser(with or without fiber coupling). The pulsed IR diode laser can employpulse durations of around 1-4 ns, and energy content of around 0.01-10μJ/pulse. The repetition rate for the pulsed IR diode fiber can be inthe kHz or MHz range (e.g., around 1 kHz-5 MHz). Furthermore, the pulsedIR diode laser can employ single pulse schemes and/or multi-pulseschemes as described in the above-referenced and incorporated patentapplications.

The laser optics 202 can include a telescope that functions to collimatethe laser beam produced by the laser source 200. Laser optics can beconfigured to provide a desired beam divergence and beam quality. Asexample, diode to mirror coupling optics, diode to fiber couplingoptics, and fiber to mirror coupling optics can be employed dependingupon the desires of a practitioner.

The beam scanner 204 is the component that provides the ladartransmitter 104 with scanning capabilities such that desired rangepoints can be targeted with ladar pulses. The beam scanner receives anincoming ladar pulse from the laser source 200 (by way of laser optics202) and directs this ladar pulse to a desired downrange location (suchas a range point on the shot list) via reflections from movable mirrors.Mirror movement can be controlled by one or more driving voltagewaveforms 216 received from the beam scanner controller 208. Any of anumber of configurations can be employed by the beam scanner 204. Forexample, the beam scanner can include dual microelectromechanicalsystems (MEMS) mirrors, a MEMS mirror in combination with a spinningpolygon mirror, or other arrangements. An example of suitable MEMSmirrors are single surface tip/tilt/piston MEMS mirrors. By way offurther example, in an example dual MEMS mirror embodiment, a singlesurface tip MEMS mirror and a single surface tilt MEMS mirror can beused. However, it should be understood that arrays of these MEMS mirrorscould also be employed. Also, the dual MEMS mirrors can be operated atany of a number of frequencies, examples of which are described in theabove-referenced and incorporated patent applications, with additionalexamples being discussed below. As another example of otherarrangements, a miniature galvanometer mirror can be used as a fast-axisscanning mirror. As another example, an acousto-optic deflector mirrorcan be used as a slow-axis scanning mirror. Furthermore, for an exampleembodiment that employs the spiral dynamic scan pattern discussed below,the mirrors can be resonating galvanometer mirrors. Such alternativemirrors can be obtained from any of a number of sources such asElectro-Optical Products Corporation of New York. As another example, aphotonic beam steering device such as one available from VescentPhotonics of Colorado can be used as a slow-axis scanning mirror. Asstill another example, a phased array device such as the one beingdeveloped by the DARPA SWEEPER program could be used in place of thefast axis and/or slow axis mirrors. More recently, liquid crystalspatial light modulators, such as those offered by Boulder NonlinearSystems and Beamco, can be considered for use.

Also, in an example embodiment where the beam scanner 204 includes dualmirrors, the beam scanner 204 may include relay imaging optics betweenthe first and second mirrors, which would permit that two small fastaxis mirrors be used (e.g., two small fast mirrors as opposed to onesmall fast mirror and one long slower mirror).

The transmission optics 206 are configured to transmit the ladar pulseas targeted by the beam scanner 204 to a desired location through anaperture. The transmission optics can have any of a number ofconfigurations depending upon the desires of a practitioner. Forexample, the environmental sensing system 106 and the transmitter 104can be combined optically into one path using a dichroic beam splitteras part of the transmission optics 206. As another example, thetransmission optics can include magnification optics as described in theabove-referenced and incorporated patent applications or descoping[e.g., wide angle] optics. Further still, an alignment pickoff beamsplitter can be included as part of the transmission optics 206.

Field Splitting and Inversion to Optimize the Ladar Transmitter's Gazeon Desirable Regions within the Scan Area:

The beam scanner controller 208 can provide voltage waveforms 214 to thebeam scanner 204 that will drive the mirrors of the beam scanner to adesired scan position pairing (e.g., scan angles). The voltage waveforms214 will define a scan pattern for the targeting of the ladartransmitter 102 within a scan area. The firing commands 214 generated bythe beam scanner controller 208 can be coordinated with the scan patternso that the ladar transmitter 102 fires ladar pulses toward desiredrange points within the scan area. Example embodiments for the beamscanner controller 208 are described in the above-referenced andincorporated patent applications.

FIG. 2B shows an example beam scanner arrangement where the positioningof mirrors 250 and 252 about rotational axes 258 and 260 respectivelydefines the targeting for the beam scanner within a scan area 254. Anincoming incident ladar pulse launched from laser source 200, comingfrom direction 256, will impact scanning mirror 250, whereupon it isreflected toward scanning mirror 252, whereupon it is reflected toward arange point within the scan area 254. The positioning of the scanningmirrors 250 and 252 will control which horizontal and vertical positionswithin the scan area 254 are targeted, and the range [depth] for thesepositions will then be extracted from pulse compression processingwithin the receiver.

In an example embodiment, mirror 250 can control where the beam scanneris targeted along a first-axis 262 of the scan area 254, and mirror 252can control where the beam scanner is targeted along a second axis 264of the scan area 104. The first and second axes may be orthogonal toeach other (e.g., a horizontal X-axis and a vertical Y-axis). Note thatthe second mirror, 252, is shown in this embodiment to be larger thanthe first mirror 250. This is because of the sweep in angles arising asthe first mirror scans, three such positions are shown in the figure. Itis desirable for compaction to introduce relay imaging optics between250 and 252 which reduces the size of the second mirror. When one orboth mirrors are scanning at a resonant frequency, the speed of the scanwill be fast in the middle of the scan area and slower at the edges ofthe scan area. This characteristic is shown by FIG. 2C, which provides atop view of the beam scanner arrangement. In the view of FIG. 2C, asmirror 250 scans at resonance, the targeting of the beam scanner alongthe X-axis 262 of the scan area 254 will be faster in the middle of thescan area than it is on the edges. The same would hold true with respectto the Y-axis 264 of the scan area 254 (where the targeting will movefaster in the middle of the scan area that is does on the edges). Thishigh rate of speed in the middle of the scan area may pose efficiencyproblems when a practitioner wants to implement a scan pattern thatincludes a large number of range points within the middle of the scanarea and/or includes interline skips/detours in the middle of the scanarea. A description of interline skips and detours in connection withladar transmitters can be found in the above-referenced and incorporatedpatent applications. This “fast in the middle” scan characteristic beparticularly acute when both mirrors are scanned at resonance so as toachieve a Lissajous scan pattern (example embodiments of which arediscussed below). Lissajous scan patterns allow for the mirrors to bescanned at high rates, and thus provides a fast moving scan pattern.However, with a “fast in the middle” scan characteristic, of which aLissajous scan pattern is a prime example, the ladar transmitter may nothave enough time to fire ladar pulses at all of the range points withinthe middle of the scan area without at least increasing the laser firingrate (which may decrease pulse energy) or including additional linerepeats in the scan pattern.

In an effort to solve this problem, the inventor discloses the use of anoptical field splitter/inverter (hereinafter “field inverter”) that ispositioned optically downstream from the mirrors 250 and 252 andpositioned to receive and re-direct ladar pulses that are outgoing fromthe mirrors so that the scan area is split and inverted in a manner thatcauses the fast portion of the scan to reside at the edges of the scanarea and the slower portion of the scan to reside in the middle of thescan area.

FIG. 3 shows an example embodiment where the beam scanner for a scanningladar transmitter includes a field splitter/inverter 300 that ispositioned optically downstream from mirrors 250 and 252 to split andinvert the scan area relative to the scan area 254 of FIG. 2B.

For the purpose of brief explanation, in this example, the beam scannerincludes mirrors 250 and 252 that may take the form of dual MEMSmirrors. However, it should be understood that other mirrors could beused for the first and/or second mirrors (e.g., galvo-meter mirrors).First mirror 250 is positioned to receive an incident ladar pulse.Mirror 250 will reflect this ladar pulse to the second scanning mirror252. It should be understood that this reflection can be a directreflection or an indirect reflection whereby the beam reflected frommirror 250 passes through relay imaging optics such as a unitymagnification telescope on its way to mirror 252. Mirror 252 ispositioned to receive the reflected laser pulse from mirror 250 andfurther reflect this laser pulse onto the field inverter mirror 300. Thereflection off this mirror can then passed through a telescope/descopeto produce the outgoing laser pulse 108 which then travels to adesignated horizontal/vertical location within a scan area 302corresponding to the range point a shot list that is being targeted bythe beam scanner.

The first and second mirrors 250 and 252 are controllably rotatablearound their respective axes of rotation 258 and 260 as discussed above.Thus, mirror 250 will be rotatable to control the position of the ladarpulse within the scan area 302 along the scan area's X-axis, whilemirror 252 will be rotatable to control the position of the ladar pulsewithin the scan area 302 along the scan area's Y-axis. Thus, thecombined positioning of mirrors 250 and 252 along their respective axesof rotation when the ladar pulse strikes each mirror will be effectiveto direct the launched ladar pulse 108 to the desired location withinthe scan area 302. In an example embodiment, the X-axis mirror 250 isscanned at resonance. However, it should be understood that the Y-axismirror 252 could also be scanned at resonance. Further still, anycombination of mirrors 250 and 252 could be scanned at resonance.

It should also be understood that one of the axes can serve as a “fastaxis” and the other axis serving as a “slow axis” to reflect therelative scan rates of mirrors 250 and 252. For example, the X-axis canserve as the fast axis, and the Y-axis could serve as the slow axis. Itshould be understood by a practitioner that the designation of the fastaxis as the X-axis and the slow axis as the Y-axis is arbitrary as a 90degree turn in position for the system would render the X-axis as theslow axis and the Y-axis as the fast axis. Furthermore, in an exampleembodiment, the fast axis mirror is smaller than the slow axis mirror interms of mirror area and is also positioned upstream from the slow axismirror (that is, the fast axis mirror receives the ladar pulse andreflects it to the slow axis mirror for transmission toward the targetedrange point). However, this configuration could be changed for otherembodiments. For example, while making the slow axis mirror larger thanthe fast axis mirror provides a benefit in terms of permitting a largerscan area, for embodiments where a decrease in the size of the scan areais permissible, the slow axis mirror could be the same size or evensmaller than the fast axis mirror. As another example, if the fast axismirror were downstream from the slow axis mirror, reimaging optics, suchas relay imaging optics, could be used between the two mirrors tosupport such an arrangement.

FIG. 3 shows an embodiment where an optical field splitter/inverter 300is positioned to receive and redirect the ladar pulse reflected bymirror 252. Thus, the field splitter/inverter 300 is opticallydownstream from mirrors 250 and 252. The field splitter/inverter 300 maycomprise mirrors or lenses that are arranged to both split the field ofview for the transmitter and invert the split field of view. Note thefigure assumes a mirror/reflector is used so the imaged scene 302 isbehind the MEMs assembly to the far right.

In an example embodiment, the field inverter 300 may take the form ofreflectors arranged in a W-shape as shown by FIG. 3 (see also FIG. 4,which is a top view of the FIG. 3 arrangement). Here, the laser pulselaunched from the second mirror, 107, is inverted and passed along tothe scene to be imaged, 302, in speed inverted fashion. The launchedpulse 108 will now be slowly scanning where 107 is fast (and viceversa).

FIG. 4 is a top view of the beam scanner arrangement of FIG. 3, and itshows the effect of the field inverter 300 on the resultant field ofview/scan area. As explained above, unlike the FIG. 1 embodiment (wherethe beam scanner scans through the scan area in a manner that is fasterin the middle and slower at the edges while mirror 250 scans atresonance (as reflected in the parenthetical shown by FIG. 4 abovemirror 102)), the beam scanner for the embodiments of FIGS. 3 and 4scans through the scan area in manner that is slower in the middle andfaster at the edges due to the field inverter 300. The beam ray path forthe beam scanner of FIGS. 3 and 4 is shown via the arrows in FIG. 4, andit can be seen that the beams which would otherwise have landed in themiddle of the scan area are instead redirected to the edge of the scanarea 400, the top view of 302, via the field inverter.

FIG. 5 illustrates the effect of the field inverter 300 on the beamfield. The top frame of FIG. 5 shows a plot of the scan speed across thefield when mirror 250 is scanning at resonance. As can be seen, the scanspeed is faster in the middle of the field than it is at the edges. Thefield inverter 300 provides a splitting effect and an inverting effect.The middle frame of FIG. 5 shows the split effect at line 500, where thefield is split into two halves. The bottom frame of FIG. 5 shows theinversion effect that operates on each of the split fields (where eachhalf defined by line 500 is inverted). For the example embodiment ofFIGS. 3 and 4, the split line 500 corresponds to the central peak of theW-shape of the field inverter. The field inverter 300 can be opticallypositioned so that this central peak corresponding to split line 500falls within the middle of the field of view. Due to the field inverter300, the beam scan path within each split field is inverted. This yieldsthe plot of scan speed across the field as shown by the bottom frame ofFIG. 5. As can be seen, the scan speed now becomes faster at the edgesthan it is in the middle of the field. This scan characteristic providesthe ladar transmitter with more time to accommodate groupings of rangepoints in the middle of a frame. Furthermore, when paired with a ladartransmitter that employs a shot list and dynamic scan pattern thatincludes interline skipping and/or detouring, this scan characteristicalso provides the ladar transmitter with more time to accommodate theline skips and/or line detours that may occur in the middle of theframe.

It should be understood that a shot list employed by the ladartransmitter would employ a re-mapping of range points on the shot listto accommodate the split and inverted field of view.

In another example embodiment, the field inverter 300 may take the forma triangular prism 600 as shown by FIG. 6A. The triangular prism 600 candefine an inverted V-shape for reflection of light pulses as discussedbelow. The example triangular prism of FIG. 6 is shown in perspectiveview and exhibits a shape that includes first triangular face 602 andsecond triangular face 604 at opposite ends of the prism 600. First,second, and third sides 606, 608, and 610 serve as the underside, rightside, and left side respectively of the triangular prism 600 shown byFIG. 6, and these sides connect the triangular faces 602 and 604. In theexample of FIG. 6A, the triangular faces 602 and 604 are orientedperpendicularly with respect to sides 606, 608, and 610, although thisneed not be the case. Triangular prism 600 can be formed from anymaterial transparent to the incident laser wavelength with the activeregions where bounce paths may occur treated with reflective material.Since empty space (air or vacuum) is transparent to ladar laser light,the prism can be hollow or dense whichever any desired manufacturingdictates.

The view of FIG. 6A is from a perspective above a laser feed 107, withpartially transparent mirrors to permit visualization of the prisminterior. FIG. 6B provides a vertical cut view into the triangular prism600 of FIG. 6A, and FIG. 6C provides a depth cut view into thetriangular prism 600 of FIG. 6A. In this example, we can take thehorizontal direction (azimuth) to be a fast axis scan which we seek toinvert, and elevation can be step-scanned or resonant-scanned. Thearchitecture of prism 600 shown by FIG. 6 is invariant to this choice.

With reference to FIG. 6A, a laser pulse 107 enters the prism 600through injection region 620. The precise site of entry 622 will vary asa result of the scanning by mirrors to define a scan pattern over a scanarea. Accordingly, injection region 620 is shown in FIG. 6A as a boxarea to indicate such range of potential entry points. After entry intothe prism 600, the pulse 107 will travel linearly until it strikes areflector mirror 624 on an interior portion of underside 606, wherereflector mirror 624 is offset in depth within prism 600. The bulletpoints in FIG. 6A show sites of reflection (or “bounce”) within theprism 600 where the pulse transiting through 600 is reflected in a newdirection. Each bounce site is labeled as I, II, or III based on anorder of bounces for the pulse 107. Thus, after striking reflectormirror 624, the pulse strikes a reflector mirror on an interior portionof right side 608 (bounce site II), whereupon the pulse 107 isre-directed to strike a reflector mirror on an interior portion of leftside 610 (bounce site III).

The laser injection angle at injection site 622 can be obliquelyselected part way from vertical to horizontal. This allows the pulse 107to bounce against both right mirror 608 (bounce site II) and left mirror610 (bounce site III) and finally to exit the prism 600 through exit cut626 and on to an exterior lens 670 (see FIG. 6C; e.g., an up/down scope)without encountering occlusions. We denote the side pitch angle formirror 608 as z+. With reference to FIG. 6B, the azimuth scan of thescanning mirrors 250 and 252 is mapped through bounce sites I-III to theangle f, 654, formed between the two dotted lines at the right hand sideof the figure. The far field angle S, 655, is formed from the anglesbetween the vertical dotted line at the right and the “flighttrajectory” of the pulse 108 exiting the field inversion assembly.Behold from congruence arguments that S=f. As in the W embodiment ofFIGS. 3 and 4, the pulse 108 is fast when 107 is slow and vice versasince the angles are reciprocally related. Our goal, if we wish to avoida gap, 500, is to set S so that the leftmost angle we can scan to isvertical i.e. S(min)=0. This ensures that the scan angle starts verticaland moves right; if it starts anywhere else the slit 500 will be large,otherwise it is negligibly small, and limited to creeping waves. Algebrareveals that

$f = {S \approx {{4z^{+}} - \frac{\pi}{4} - {\phi.}}}$

(see 654 text). When the scanning mirror azimuth scan is set to ℠=0[where the trajectory of 107 is fastest], we see that the launched pulse108 is sent to

${4z^{+}} - {\frac{\pi}{4}.}$

Likewise when the scan is at its angle we obtain

$S \approx {{4z^{+}} - \frac{\pi}{4} - {\phi_{\{{{ma}\; x}\}}.}}$

Thus we obtain

$\phi_{\{{{ma}\; x}\}},{= {{4z^{+}} - \frac{\pi}{4}}}$

as the desired mirror pitch angle. This completes the field inversionprism shape's exterior 602-610 as it relates to pre-inversion scan angleand scene azimuth positioning. It remains to discuss the prism internalstructure and elevation scan.

Referring to FIG. 6C, it can be shown by algebra that the choice ofinjection angle c [the vertical angle for the scanning mirror outputpulse 107], 675, will produce a desired far field elevation scan angleof this exact same value, that is c, 675, equals the depression angle ofthe ray 670. As the injection elevation angle c varies from c′ to c, itsweeps through angle e, 673, the elevation swath of the scanning mirror.The bounce point I in FIG. 6C will then move along the prism base 674.It should be clear that the length of this sweep determines the extentto which the mirror interior must be treated with a reflective surface.The entire prism apparatus can be scaled by an overall scale factor toaccount for the projective geometry. Specifically the pulse launch fromthe prism will travel along the vector t sin(c)[sin(4z−ϕ), cos(4z−ϕ),cot(c)]. We can see that we can treat the x,h analysis as a twodimensional problem and afterwards correct by a scale factor of sin(c).This observation is in fact what enabled us to decompose the probleminto x,h then y,h in the first place, as done previously.

Also shown in FIG. 6B is a dotted line 660 traversing the injection site622 at the horizontal axis of symmetry This dotted line 660 is nottraveled by the laser, but is a virtual path that is able to replace theactual path for the first bounce site I in modeling. The virtue of sodoing is the geometric mathematics then greatly simplifies. One canobserve that the laser pulse 107 arriving from the scanning mirror willcome from different locations by virtue of the different points onmirror 252 that are illuminated. The fact that 107 moves aboutcomplicates the math, and it is much easier to invoke symmetry and“pretend” the laser pulse originates from point 650 with differentarrival angles.

We can now introduce some notation. We can denote the horizontaldirection as x, the elevation as h (height), and the depth of the prism,i.e. the distance along the line connecting 602 and 604, as y. With thisnotation, FIG. 6A shows the prism 600 with sides 602,604 in the x,hplane and the underside lies in the x,y plane. Next, we introducesubscripts l,r to denote the left and right side mirrors 610 and 608respectively. This means that the mirror pitch angle can be representedas z where

$z^{\pm} \equiv {\frac{\pi}{4} \pm {z.}}$

This notation simplifies a mathematical representation of prism 600.Recall, the pitch angle of the V shape is z⁺, and the internal angleinside the V shape (which is the angular complement of z⁺) is z⁻. Thefield inversion is defined via the mathematical dance which the laserangles undergo as the follow through these angles. Recall, the notationf, 654, denotes the scan angle in the horizontal direction that wedesire in the far field, which also happens to equal S, 655. Thenotation c′ denotes the steepest downward injection angle (when thepulse 107 travels path 672) used in the elevation scan (as measured fromthe vertical axis on FIG. 6A). Recall that the notation c is the tunablefar field elevation angle, ranging from zero to e, 673 (see FIG. 6C), asmeasured against the horizontal plane (see the horizontal axis in FIG.6C). We introduced the notation is 4), the azimuth scan angle at a pointin time that the second scanning mirror 252 output pulse furnishes atthe laser injection site 622. Recall it can be seen that the far fieldangle f can be expressed as f≈4z−ϕ. By symmetry, the same behavior willarise if we begin scanning right versus left, with left and rightdefined as shown in FIG. 6B. Since ϕ has been inverted, the prism 600achieves splitting and inversion.

Furthermore, to demonstrate that the prism 600 can be blockage-free, wecan lift the scaling. FIG. 6C shows a depth formula for yr as anintermediate to calculate input/output invariance, 673. This formula canbe used to position an exterior descope/telescope lens 670 beyond thelast bounce III as measured in depth.

If desired by a practitioner, a position sensor (not shown; e.g., a 4quad position sensor) can be positioned near the second scanning mirror252 to precisely determine the scan position of mirror 252, which allowsfor calibrating out material defects beyond the above formula for f.This calibration can be achieved by adding a secondary wavelength intothe pulse 108 and placement of a frequency/wavelength-selective mirror(e.g., a dichroic mirror 674) near the injection site 622. This mirrorcan selectively reflect light at the secondary wavelength to theposition sensor for accurate detection of the scan position for mirror252 over time. A dichroic mirror can also be used to calibrate thescanning of mirror 250 if desired by a practitioner.

Also, Taylor series applied to the far field angle S will reveal thatfor all practical purposes:

${\delta f} = {{{- \delta}\phi} - {\delta{\frac{\phi^{3}}{2}.}}}$

This formula can be used to construct the morphing of the far fieldpattern, i.e. obtaining a desired corrected angle S by adjusting thescanning of mirror 252 and mirror pitch angle z+. Any corrections beyondthis point can be masked by calibrating out imperfections in the opticalassembly for most and perhaps any diffraction-limited commercialsystems. As noted above, such calibration can be achieved by thedichroic mirror 674. By correcting time warping analytically, the rangeand sophistication of the time warping calibration that relatessinusoidal scan mirror control signals to the scan position in the farfield can be greatly simplified.

Also, it should be understood that the right and left mirrors 608 and610 can be selected to be one-way in their entirety or over injectionregion 620 to allow the injection region 620 to also be a potentialbounce site. This repurposing of the same physical mirror real estatecan lead to a more compact design, thereby saving cost, weight, and sizefor a practitioner. As a minimum for an example embodiment, we canrequire that the segment of the prism side-traced by the bottom of the Vto point 622 in FIG. 6B must by two-way, as must be the mirror image onthe other side of the V. The reason for this is that as ϕ gets nearzero, we want a bounce back when moving from plate 624 towards 660,while we also want an absence of a bounce at the bottom of the V whenmoving in the opposite direction.

Furthermore, ray tracing can be used to determine which regions of theprism interior might serve as bounce sites for laser pulses 108 duringoperation. The left half of FIG. 7 shows the xl,yl (left side of plot)and xr,yr (right side of plot) ray tracing and region lased in the exitwindow 626 across the scan volume, shown in mm, for a 1 mm interscanning mirror spacing and a V slot base to reflector dimension of 1mm. The x-axis of 702 can be used to select the L-R mirror x-axis (610,608) onset and the 704 x-axis as the mirrors 610, 608 y-axis onset. They-axis of 706 can be used as the terminus in depth. As shown in theright half of FIG. 7, we can use the x,y position of 708 to be thebeginning (inner terminus) of the exit window 626 and we can use the x,yposition of 710 as the end (outer terminus) of the exit window 626. Weuse the exit window embodiment here to be constant height so the bottomof the prism 606 is coplanar with exit window 626, which is directlyattached to an up/downscope. However, it should be noted, cantedinterfaces with the up-scope may be chosen as compaction might require,and the ray tracing can still be employed to determine requirements onprism dimensions and one-way mirror minimum areas. Thus far, we havedefined the rectangular boundaries of mirrors 610/608/606. The portionof the mirror cavity that never receives bounces I, II, or III can nowbe eliminated. This can be accomplished by computing the contours tracedout by 702, 712, 706 and 704, 710, 714 and assigning mirror (i.e.,reflective coating) to the attendant convex hull varying over all setsof angles. The mirror need only be one-way over the region determined byray tracing x,r of the scanning mirror output over their scan angles.Through this process, mirror compaction can be achieved which may reducemanufacturing and raw material costs.

Overlapped Inversion/Splitting:

The field inverter 300 can also be configured to provide aninverted/split field of view that is overlapped. This configuration notonly decouples mirror inversion with field look direction but alsoallows multiple mirror inversions per field look direction within asingle axis scan. This overlapping effect allows for a longer gaze alonga desired region such as a middle region or centerline of a field ofview. Accordingly, it should be understood that the field inverter 300need not split the field of view into two non-overlapping fields. Toachieve overlapping, the mirror pitch angle z+ can be modified so thatthe launch angle of pulse 108, i.e. angle S swings negative (i.e. leftof vertical) at extremal values of the scan angle ϕ.

By creating an overlap, we exchange high elevation scan time for doublerevisit of the specified foviation zone, which allows a deeper look downthat can be useful for avoiding near obstacles.

An example of this arrangement is shown by FIG. 8. In this example, wechoose to field invert the scan on azimuth (the horizontal axis), with aselected scan volume of 45 degrees,

${A_{az} = \frac{\pi}{4}}.$

Without field inversion, the relation between the x-axis, the resonantscan angle for mirror 252, and the vertical axis, the far field scanangle f would be identical—i.e., =A_(az).

With field inversion, we observe that as the resonant mirror scan anglegoes from −22.5 degrees to zero, the fair field scan angle f ranges fromzero to −22.5 degrees. This “flip” is expressed mathematically by theformula for f, where there is a shift (4z) and a negative sign relatingthe vertical to horizontal axis. The moment the mirror scan moves from0− to 0+, the far field scan angle f flips from −22.5 degrees to 21degrees. In the absence of overlap, this flip would end up at 22.5degrees rather than 21 degrees. The difference between overlapped andnon-overlapped scans can be defined and achieved in real-time with ahinge as discussed below. Since we begin the far field scan angle at 21degrees, and we must swing through 22.5 degrees net in the scanningmirror, we end at −1.5 degrees in the other direction (as opposed tozero as we would for non-overlapped field inversion). It is this changethat provides the beneficial effect of overlapping because we now scanthrough the horizon twice for each scan leg (where it is expected therewill be a need for more range point detection).

The horizontal axis of FIG. 8 is the angle to which the scanning mirror(e.g., MEMS mirror) is “looking”. Because the scanning mirror is slowestwhen it changes direction, we can see from the curve at the top of FIG.8 that the scanning mirror is moving fastest at the center (0 degrees).It is also moving slowest at the edges of the scan (in this example at−22.5 degrees and 22.5 degrees). As discussed above, this can beproblematic for practitioners when the center region is the area whereit is desirable to maximize gaze time (to increase how many range pointsare lased in the center region) (e.g., for automotive applications, thecenter region is where most accidents are likely to occur). The verticalaxis in FIG. 8 is the location in the far field where the ladartransmitter is gazing, i.e. the instantaneous field of view. In atraditional, non-inverted field of view, this gaze location would beequal to the horizontal axis. If zoom or upscope is added to the ladartransmitter, the relationship remains linearly proportional. This meansthe “bad” edge gaze of the scanning mirror is “inherited” in the ladartransmitter's gaze into the scene. Since the scanning mirror's scanposition alone determines where in the scene that the instantaneous gazeis located, there is a curve that we can plot that represents therelationship connecting these two axes. While the example of FIG. 8 isshown for only one resonant scanning mirror, the same idea works for 2Dresonant mirror scanning but is more complex with respect toarticulation, so for ease of illustration the single resonant scanningmirror example is shown. For standard non-inverted ladar transmitters,this relationship curve is simply a straight continuous line. However,with field inversion, as shown by FIG. 8, the curve is presented by twoline segments with a “jump” reflected around the vertical axis. The endresult is seen in the plot of the speed of the instantaneous field ofview within the scene to be imaged at the far right of FIG. 8. Relativeto the top plot of FIG. 8, the speed is inverted vis a vis thehorizontal, MEMS axis. Indeed, we now stare a relatively longer time at0 degrees (where speed is slow) and spend relatively less time at thescene edges (where speed is high).

With regard to overlapping the inverted view, we can choose to scanbeyond zero at one or both edges of the mirror scan. FIG. 8 shows anexample where the right hand scan (and only the right hand scan in thisexample) is selected for overlap. One can see that the scene isinspected a 0 degrees and down to −1.5 degrees on the right hand scan,which increases the amount of time we gaze at the centerline of 0degrees and environs via overlapping.

To control and adjust how much overlap is achieved, one or morecontrolled hinges 628 can be used to define the mirror pitch angle z+,as shown by FIG. 6D. Hinges 628 allow for the mirror pitch angle of theprism 600 to be adjusted. A mirror pitch angle adjustment mechanism(such as a threaded knob arrangement 630 and 632 by which the mirrors608 and 610 are pivoted at hinges 628 to adjust the mirror pitch angle)can be used to slide mirrors 608 and 610 along base 606. This results inthe ability to dynamically adjust the degree of backscan and or theField of View in real-time, at sub-second rates. By adjusting the mirrorpitch angle z+, the scan volume and overlap of the field inverter isdynamically controlled. Specifically, the midfield and far field anglesS and f become tunable using a mechanical actuator to adjust theintersection of right and left mirrors 608 and 610 with the planesubtending the reflector 606.

It should be understood that still other embodiments for a fieldinverter 600 could be used by a practitioner. For example, the reflector606 could be replaced with a scanning mirror to add more compaction andshrink the spans shown in FIG. 7 in exchange for potential occlusionfrom non-reflecting material at the boundary of 606. Another example isto use two resonant mirrors designed to scan a left and right angularinterval, with a potential overlap. The right hand edge of the leftmirror and the left hand edge of the right mirror can then serve asfield inverters. An example of this is shown by FIG. 20. FIG. 20 shows alaser 2000 which is common to each of the scanning mirrors 2010 and 2012(e.g., MEMS scanners in this embodiment). Shown is a single scan axis,the orthogonal axis is scanned through a field inverter, a standardscan, with a common mirror, or independent mirrors as deemed desirableby the practitioner. Laser output 2002 is fed into a beamsplitter 2004.As examples, The splitter 2004 can be a WDM (wave division multiplexer),a MEMS switch, Pockel switch, etc. To the right of the splitter 2004, wehave a scan mirror 2010 with a scan sector shown by the dotted lines,beginning at directly forward 2014 to a far right hand direction 2018.To the left of the splitter 2004 is the other scan mirror 2012 with ascan sector shown by the dotted lines, beginning at directly forward2016 to a far left hand direction 2020. Since the speed of scan isslowest at the edges of the scan, it is evident that arrangement of FIG.20 implements an inverted field.

FIG. 9 depicts a table that demonstrates the effect of increased gazetimes that can be achieved via field inversion (non-overlapped) andoverlapped field inversion. The table of FIG. 9 is based on a 90 degreescan range, and it shows the results of measuring the time spent nearthe centerline (within 3 degrees of the centerline) over each scan for astandard operation (no field inversion), field inversion operation(non-overlapped), and an overlapped field inversion (with a 1 degreesplit field for 5 mrad beam divergence). As can be seen, field inversionand non-overlapped field inversion yield significant improvements indwell time near the centerline.

Lissajous Scan Patterns with Induced Periodic Phase Drift:

A 2D laser scan pattern is called a Lissajous scan pattern if and onlyif the 2D beam scans sinusoidally (in time) along each axis. The phaseof both azimuth and elevation can be arbitrary, but are fixed in astandard Lissajous scan. The Lissajous pattern is generally desirablewhen one wants the fastest possible scans. This is because the fastestmirrors are resonant mirrors which must be driven periodically andresonantly, and hence sinusoidally. Thus, in a Lissajous scan pattern,both mirrors 250 and 252 will be driven by sinusoidal signals. Whileboth phases of these sinusoids are free, the difference between themimpacts scan performance. The usual choice for the phase differenceamongst practitioners is 90 degrees, which minimizes the maximum gapbetween where adjacent beams scan.

The Lissajous can pattern for a 2D resonant beam scanner can beexpressed as:

[height(t),azimuth(t)]=[A _(h) sin(ft),A _(az) sin((f+1)t+ξ)]  (Eq1)

The resonant frequencies f,f+1 differ by only 1 in many applications asthis is well-known to minimize gap times. However, for ladar in a roaddriving context, other choices might be desired, due to the fact thatazimuth rate of change and elevation rate of change differ for objectson the road surface.

FIG. 10A depicts an example of a Lissajous scan pattern for a ladartransmitter when no field inverter 300 is employed. FIG. 10C depicts therevisit performance of the Lissajous scan pattern of FIG. 10A. The axesin FIGS. 10A and 10C are an X-axis corresponding to horizon/azimuth anda Y-axis corresponding to elevation. In FIG. 10C, the Z axis is thenumber of revisits per Lissajous cycle, with periodicities 99,10, foroverall Lissajous cycle of 990. The scan range chosen here is 45 degreesin each axis. For physical fidelity uniform phase drift of half the beamdivergence of 9 mrad was added. In addition a road surface was added,with lidar velocity of 30 m/s, with an above horizon slice of 4 m.Motion is included because the true revisit must take this variable intoaccount. However, this component has only a minor effect.

The lines in FIG. 10A are a tracing that shows where the ladartransmitter is targeted as the mirrors scan. The white regions are thespacings or gaps that would exist between beams that are theoreticallyfired all along the scan lines. The surface mesh in FIG. 10C shows howthe revisit rate varies as a function of azimuth and elevation. Forexample at the edges we obtain about 8 opportunities to revisit a pointper cycle. This aspect of FIG. 10C shows the “downside” of aconventional Lissajous curves for ladar: the best revisit is at the edgeof the scan volume, where it is least needed. Specifically, the plots ofFIGS. 10A and 10C show how a standard Lissajous scan results in denservisits at the edges of the scan area relative to a center region of thescan area. That is, FIGS. 10A and 10C show that there are larger gapsand delays between the scan lines and opportunities in the center regionof the plot than there are at the edges. Again, this is contradictory tomost desired applications (such as most automotive applications) wheredenser visits are desired at the center region.

As mentioned above, a field inverter 300 such as prism 600 can be usedto split and invert a scan pattern, which when applied to the Lissajousscan patterns of FIGS. 10A and 10C yields a scan pattern with increasedgaze time near the center region, as shown by the example of FIG. 10B.FIG. 10B depicts an example of a split/inverted Lissajous scan patternwhen a field inverter 300 is employed to provide inversion along thehorizon (i.e., the horizontal axis when the elevation is zero), and FIG.10B shows that the density of visits by the ladar transmitter near thecenter line is greatly increased relative to that of FIG. 10A. Thisdifference is dramatic, as the gaps along the horizon are virtuallyeliminated.

FIG. 10D depicts a plot of revisit performance for an example of asplit/inverted Lissajous scan revisit when a field inverter 300 isemployed to provide inversion along elevation (i.e., the vertical axiswhen the horizon is zero), as well a kissing mirror pattern in theazimuth direction. FIG. 10D shows that the density of visits by theladar transmitter near the center line is greatly increased relative tothat of FIG. 10C. This difference is also dramatic, there is roughly 20times more access to the horizon directly in front of the ladar-equippedvehicle.

Another way to measure the significance of these gaps is to determinewhich gaps exceed a defined threshold. This threshold can be definedbased on beam divergence to account for the profile/diameter of a laserpulse 108 at an assumed distance with respect to a targeted range point.If the gap is larger than the threshold, this would represent apotential blindspot that could not be targeted by the ladar transmitter.However, if the gap is smaller than the threshold, such a small gapcould be subsumed by a laser pulse 108 targeted nearby. FIG. 11A shows aseries of dots which represent potential blindspots for the ladartransmitter when a Lissajous scan pattern such as that shown by FIGS.10A and 10C is employed (with no field inverter 300), now withperiodicity 48,49. As can be seen, there are a relatively large amountof blindspots in the center region of the plot. FIG. 11B shows thecorresponding blindspot plot for the inverted Lissajous scan pattern,such as FIG. 10B (once again, where each dot represents a potentialblindspot) but now with periodicity 48,49. As can be seen by FIG. 11B,the combination of the field inverter 300 with the Lissajous scanpattern yields a ladar transmitter with a significant blindspot-freezone in the center region.

However, FIG. 11B shows that blindspots do exist in the split/invertedLissajous scan pattern in regions outside the center region. This raisesthe question of how the system can be design to reduce the extent ofsuch blindspots, ideally in a manner that allows the system tointelligently select desired regions for increased gaze that are notnecessarily inside the center region.

As solution to this problem, the inventors disclose the use of aninduced periodic phase drift in the Lissajous scan pattern. With thisapproach, the fixed phase that is common in Lissajous scan patterns isreplaced with a time-varying drift. One (or both) of the scanningmirrors 250/252 is driven slightly off resonance by gently varying itsphase. Accordingly, with this embodiment, we can represent the phase as(t) rather than as shown above by Equation 1 in the formulaicrepresentation of the Lissajous scan pattern. This phase drift (t) isinduced by having the beam scanner controller slowly vary a commandsignal provided to a driver for the subject scanning mirror (e.g., wherethe driver could be a motor for a stepped scan or a piston for a MEMSmirror). This command signal controls the mirror with respect to how itscans. In an example embodiment, the phase drift can be represented as:

ξ(t)=Σ_(i=1) ^(M/2) A _(i) sin(K _(i) t+μ _(i))  (Eq2)

Accordingly, the Lissajous scan pattern as modified to include theinduced periodic phase drift in both dimensions can be represented by:

$\begin{matrix}{\left\lbrack {{{height}(t)},{{azimuth}(t)}} \right\rbrack_{drifted} = \left\lbrack {{A_{h}{\sin\left( {{ft} + {\sum\limits_{i = 1}^{M/2}{A_{i}{\sin\left( {{K_{i}t} + \mu_{i}} \right)}}}} \right)}},{A_{az}{\sin\left( {{\left( {f + 1} \right)t} + {\sum\limits_{i = {1 + \frac{M}{2}}}^{M}{A_{i}{\sin\left( {{K_{i}t} + \mu_{i}} \right)}}}} \right)}}} \right\rbrack} & ({Eq3})\end{matrix}$

In this expression, we denote M as the total number of phase frequencydrift components across both mirrors. We can take all M drift componentsand apply them to one of the scanning mirrors, or as shown in the aboveformula, we can distribute the phase frequency drift components acrossboth scanning mirrors. This distribution can be an even distribution orsome other distribution. It should be understood that even with a singleresonant mirror, a system can still benefit from the induced drift interms of increasing gaze time in targeted regions, although we willdescribe the example embodiment in terms of two mirrors scanning atresonance. For a linearized approximation of Equation 3, associated withsmall amplitudes A_(i), we have:

$\begin{matrix}{\left\lbrack {{{height}(t)},{{azimuth}(t)}} \right\rbrack_{drifted} \approx \left\lbrack {{A_{h}\left( {{\sin({ft})} + {{\cos({ft})}{\sum\limits_{i = 1}^{\frac{M}{2}}{A_{i}{\sin\left( {{K_{i}t} + \mu_{i}} \right)}}}}} \right)},{A_{az}\left( {{\sin\left( {{ft} + t} \right)} + {{\cos\left( {{ft} + t} \right)}{\sum\limits_{i = {M/2}}^{M}{A_{i}{\sin\left( {{K_{i}t} + \mu_{i}} \right)}}}}} \right)}} \right\rbrack} & ({Eq4})\end{matrix}$

For this example discussion, we can set M=4 to simplify the narrative,and we will ignore phase drift terms μ_(i) with the understanding that,for the example embodiment where a total least squares approach is usedto find the desired drift, the terms μ_(i) behave just like the driftfrequency terms K1, . . . during optimization and actuation.

It is also advantageous for the phase drift to be periodic with aharmonic sub-period of the initial pattern, i.e., where

$\frac{K_{i}}{f},\frac{K_{{M/2} + i}}{f + 1}$

are rational and less than unit modulos. This assures that the revisittime is not reduced, thereby ensuring that the gap reductions are notachieved at the cost of a slower pattern revisit time.

With regarding to choosing the periodic drift frequencies Ki, there willbe tradeoffs involved. If we choose periodic drift frequencies Ki thatare too close to the Lissajous frequency f, then there will be verylittle effect on the pattern because the phase rate of change will blurinto the frequency. Also, if the drift frequency is too low, the phaserate of change blurs into the fixed phase term of the Lissajous pattern.In the examples presented below, we describe an embodiment where thedrift frequencies are set to lie at the midpoint prior to iteration.However, it should be understood that these are examples only and othervalues could be chosen.

In an example embodiment, an optimal phase for fixed drift frequency isdetermined as a solution to a total least squares problem. Total leastsquares (TLS) fits parameters when both dependent and independentvariables are free, which will be the case here with the independentvariable for TLS being time. The minimization employs a cost function.As an example, consider automotive ladar where we select a region in theground plane as the area where we wish to remove gaps.

FIG. 12 discloses an example process flow for controlling how a scanningmirror is induced with a periodic phase drift. Driver 1250 for ascanning mirror includes an actuator which can periodically modulate thephase ξ using parameters A_(az), A_(h)A_(i)K_(i)μ_(i), i=1, . . . , Mwhile retaining the frequencies f,f+1. Step 1204 in FIG. 12 describesframe-dependent feedback in the scan pattern for the scanning mirrorcentered on total least squares The use of singular value decomposition(SVD) assures that the FIG. 12 process flow can be executed inreal-time, specifically on the order of milliseconds.

At step 1200, the process flow is initiated via selection of systemparameters. As part of this, the minimum acceptable ground gap isdefined. This can be set as an angle or a distance in meters. We chosethe gap in meters for an example embodiment. We compute the gaps bylooking at where the pulses can be fired from scan to scan, andmeasuring if the distance is larger than this amount, measured as anextent beyond the full width half maximum of beam divergence. We declarea gap, and use that gap in calculating phase drift when, as shown in1202-1204, the gaps are (i) larger than 1 m, and (ii) within thepreferred scene (gaze region) Q. Examples of this are shown in FIG. 13A(for a non-inverted case) and FIG. 13B (for an inverted case), wheref=49. The black regions in FIGS. 13A and 13B (e.g., see 1302) are theregions in the x,y axis which are further away than 1 meter by 1 meterfrom a laser pulse for all values of time t in Equation 1 above. In thisexample, the ground plane is used to determine gaps. However, in anotherembodiment, one could use the azimuth elevation plane for identifyinggaps, in which case we would use the black cluster in FIGS. 11A and Brather than FIGS. 13A and B.

Next, the drift frequencies are selected (where, for M=4 in thisexample, 2 drift frequencies are used for each scan axis). We alsoselect the Lissajous frequencies f,f+1, field of view (FOV) and thetolerable gap size. The Lissajous frequencies will be set by thetransmitter control instructions, 103. The FOV will be determined by thespeed of the mirror scans as well as the desired region we wish thelaser to inspect, coupled with the gaps. For example, if the maximumscan frequency is 10 Khz, and we scan across 100 degrees, with 1microsecond pulse spacing, the gaps will be about three degrees, if wescan across 20 degrees at 10 microseconds the gaps will be 4 deg. Forexample, with FIGS. 13A and B, the FOV is +/−45 degrees in azimuth (asevidenced by the slope of black triangle 1304). Likewise, the verticalFOV ranges from the horizon down to 12 degrees, as evidenced by thesmall black rectangle 1306 near 0,0 assuming a 2 meter height monitoringof the ladar transmitter.

For the purposes of phase drift, the only part of the FOV that mattersis the range below the horizon, so the upper limit of the elevation FOVbeyond zero is immaterial (as indicated in FIG. 13A by no black dotsbeing shown above 1600 feet and in FIG. 13B by no black dots being shownabove 800 feet).

At step 1202, we generate the standard fixed phase Lissajous patternaccording to the defined parameters. FIG. 13A shows the gaps for astandard Lissajous pattern where f,f+1 is 49,50 and no inversion takesplace, and FIG. 13B shows the gaps for a standard Lissajous patternwhere f,f+1 is 49,50 and where inversion with a 1 degree overlap takesplace. FIGS. 11A and B show the respective gaps in the vertical (laserline of sight) for the non-inverted and inverted space for a 3 mrad beamwidth, and FIGS. 13A and B show these same gaps projected onto theground plane with a one meter gap tolerance. Region 1310 shows gazeregion Q where gap reduction is desired. The gaze region enters into theprocessing stream in FIG. 12 in section labeled 1202. Only the gaps inthis section are used in the subsequent algorithm stages, all otherregions are ignored. In our example all the gaps are removed in 1310,which is why we labeled them grey. Region 1310 can exhibit any shape,and it can be selected based on the environmental scene (see 120 in FIG.1B). For example, consider a case where we have a side road that we wishto scan near its intersection of a ladar transmitter-equipped vehiclewhich is moving, along azimuth=0, from 0 to 800 feet where theintersection arises. The Q selection might be either data adaptive (weobserve traffic moving along the region 1310 and seek to investigate) orit may be selected from a priori information (such as a road networkmap). The size of M will determine the rate of change for the Q selectinthat is allowable in real-time. Preliminary work indicates that M=4works quite nicely and easily converges in time to update at amillisecond rate. In our example, the projections are to a ground plane,but it should be understood that any projected surface will do,incorporating terrain elevation or other considerations that mightreplace ground planes with other topological manifolds.

The detected gaps that exceed the defined minimum accepted gap aregrouped into a set of points as S. Thus, S will be a collection ofpoints that represent the black dots 1302 in FIG. 13A (or 13B).

Next, Equation 1 is used to find the times t that are yield coordinatesthat are closest to each point in S. These times can be denoted in theset T.

Step 1204 follows where we solve the TLS solution using the principalcomponents from steps 1202 and 1204. In the following description, wewill restrict the embodiment to ground plane gaze, with field inversionand overlap. First, we linearize using Equation 4 with times t set basedon the elements in T. The TLS solution will pick pairs A_(i), μ_(i). aswell as updated time stamp T based on the linearized Taylor seriesrepresentation of the drift. We can now substitute these values intoEquation 3, and from this find the new (generally smaller) set of blackdots that define a new set which we will denote as S_drift. Next, werecurse again, resolving TLS over time stamps, amplitudes, and driftphases and frequencies until a desired performance level is achieved.

As per step 1210, if at any point S or S_drift is zero, we inject thephase drift controls corresponding to that S or S_drift into driver1250. There are two mutually exclusive and collectively exhaustiveoutcomes of this procedure. The first is that the set in S no longershrinks (see step 1212), in which case we can update the Lissajousparameters [K,f] and repeat to test if performance improves (S,S_driftis reduced). Alternatively, S,S_drift reduces to a size that is deemedworthy of termination (or vanishes entirely).

For an example run, all of the black dots in region 1310 of FIG. 13B canbe removed (i.e., S_drift is empty). The example run took only 1 Mflops,executable in 1 ms for 1 Gflop processor, which is fast enough to beupdated on a single frame basis. The zoom of the field inverted andphase drifted overlapped pattern is shown by FIG. 14A. FIG. 14B showsthe corresponding non-phase drifted Lissajous pattern. FIGS. 14A and Bzoom in near the horizon since that is where the main activity occurs,and an inspection of FIGS. 14A and B reveals clues as to how the inducedphase drift improves performance and removes gaps. First, we note thatin both cases the scan range region is shown in expanded view since thefull view plot in FIGS. 10A and B is too coarse to garner insight. Next,we note that there is a lot of scanning slightly below the horizon, andthis region has very tight spacing between laser scans. This is combinedfeature of both field inversion and overlapped coverage, common to bothexamples. In both cases we have chosen to tune the two mirror fieldinverter to place renewed emphasis on the elevation scan between about−0.3 degrees and −1.2 degrees in elevation. Inspection of FIG. 14A showsthat within the dense scan region and the coarser scan region (above−0.2 degrees elevation and below 1.2 degrees elevation), thediamond-shaped gap regions are irregular, and more irregular than inFIG. 14B. This is the gift that the FIG. 12 process flow bestows bydetermining the best way to drift the phase so as to drive down the setS. Also, we note that the vertical stripes in FIG. 14A are more spacedapart than they are in FIG. 14B. This is a result of the phase driftbifurcating the revisit pattern and replaced diamond gaps with tightergaps.

Accordingly, it should be understood that the induced phase drift can beused to intelligently selection regions of the scan area for longerdwelling gaze. Moreover, when combined with a field inverter 300, theuse of mirrors scanning in a Lissajous pattern with induced phase driftis expected to provide significant performance improvements that allowsfor better interrogation of desirable regions in a scan area per frame.

Ellipsoidal Reimaging Mirror for Compact Beam Scanner Assembly:

The inventors recognize that there is also a desire in the art forcompact beam scanner assemblies. For example, the inventors believethere is a growing interest in compact 2D scan mirrors for automotiveand airborne ladar, biomedical imaging (i.e. endoscopy), virtual andaugmented reality, and confocal active imaging. Scan mirrors, whetherimplemented as galvanometers, MEMS, or other mirrors, are often used inlaser scanning systems due to the associated high scan speed and compactform factor. The fastest real scan rate and tilt angle is usuallyobtained by cascading a pair of in-plane and out-of-plane single axis(as opposed to dual axis) MEMS devices. The second mirror in the lightpath has a larger spot size than the first due to beam divergence. Theinventors disclose a device which reimages the spot beam on the secondmirror, thereby shrinking the required mirror size. Not only does thisreduce the form factor of the scanner, it also increases scan speed,and/or maximum tilt angle, and therefore scan field of view, sincemirror area is proportional to torque and scan speed.

In an example embodiment, two scan mirrors (e.g. MEMS mirrors) can beplaced at the foci of an ellipsoid defined by an ellipsoidalreflector/mirror. A focusing lens (or mirror) can be positioned tocondition the input beam prior to directing the beam onto the first scanmirror in order that the output beam can remain collimated. This isoptically equivalent to placing an image of the first scan mirror at thelocation of the second scan mirror, a situation known as being opticallyconjugate. For this reason, the reflector assembly can be referred to asan elliptical conjugate reflector (ECR) assembly. In an exampleembodiment, only a relatively small portion of the complete ellipsoidwill intercept light reflected from the first scan mirror, as determinedby the angle of incidence of the light beam at the first scan mirror.This allows construction of the ECR using only the corresponding sectionof the ellipsoid. This in turn provides a ready mechanism for allowingboth the incoming and outgoing light beams to enter and leave theassembly.

Analysis of the imaging properties of the ellipsoid shows that the angleof incidence at the first scan mirror can be chosen so that thereflected ray fan from the first scan mirror towards the reflectingsurface of the ellipsoid interior is oriented so that the intersectionof all the rays in the ensuing fan lie in a plane which also containsthe center of the second scan mirror. We disclose a design formula thatensures this coplanar dependency, with or without a tilt offset on thescanners. A tilt offset allows for flexibility in the length, height,and width of the assembly, which has the benefit of increasing thetrades available to a practitioner.

In addition to 2D scan applications, the ECR techniques disclosed hereinoffers improvements in any cascaded mirror assembly. Cascaded mirrorsincrease overall scan aperture, and the reimager disclosed hereinrenders these systems more compact as well. In contrast to prior art,the ECR solutions disclosed herein provide a more compact solution (see,for example, an embodiment that uses a single mirror for reimaging)without introducing artifacts into the scanned field.

A laser can be scanned with a pair of single axis mirrors. If themirrors are attached to a solenoid, this is referred to as agalvanometric scanner. In many modern compact laser systems (whichincludes copy machines, bar code readers, and ladar systems), MEMSsingle chip devices are often used as the tilt mirrors to reduce size,weight, and cost, while increasing scan speed. Since it is desired thatthe mirrors freely articulate, and the light cone communicating betweenthem be unoccluded, there are hard constraints on how close the distancebetween the articulating mirrors can be. Since the second scan mirrormust be large enough to accommodate the entire range of angles inducedby the first scan mirror, it is conventional that the second scan mirrorin general be larger than the first scan mirror. This in turn reducesachievable maximum scan angle, or maximum achievable scan frequency, orboth. Since both are important design parameters for practitioners ofthe laser arts, the inventors disclose in an example embodiment a designthat allows a significant increase in scan volume by rendering a systemwith two scanning mirrors (such as MEMS devices) of small and equalsize. The limitation on mirror size is a function of both laser beamwaist and scan volume. Reimaging allows a MEMS device on the order of afew millimeters. To solve this problem in the art, the inventorsdisclose the use of an ellipsoidal reimaging reflector that ispositioned optically between the first and second scan mirrors. Such adesign can preserve the simplicity of planar MEMS mirrors as thescannable mirrors while also offering improved performance. Moreover,this ellipsoidal reflector can be the single reimaging mirror used bythe system.

FIG. 15 shows an example embodiment of a design employing an ellipsoidalreflector 1510. The reference H. Rehn, “Optical Properties of EllipticalReflectors”, Opt. Eng. 43(7) 1480 (2004), the entire disclosure of whichis incorporated herein by reference, provides additional detailsincluding optical properties associated with an ellipsoidal reflector.It should be understood that when reflector 1510 is referred to as anellipsoidal reflector, this means that the reflector 1510 exhibits acurvature that corresponds to at least a portion of an ellipsoid shape.Thus, the ellipsoidal reflector 1510 preferably exhibits a shape andcurvature corresponding to a section of a hollow ellipsoid. The examplesystem shown by FIG. 15 uses the ellipsoidal reflector 1510 in an offsetconfiguration. Also, in an example embodiment, the specific ellipsoidalstructure used for reflector 1510 can be a prolate spheroidal shape.Such ellipsoids have rotational symmetry about the major axis, and thisstructure allows physical separation of the two scan mirrors.

Consider an ellipsoid of revolution defined by the formula

${{\frac{z^{2}}{A^{2}} + \frac{r^{2}}{B^{2}}} = 1},$

where r′=x²+y². The projection of this into a plane is an ellipse 1550with horizontal length of 2A (see 1520 in FIG. 15 which identifies thelength A), and vertical height 2B (see 1526 in FIG. 15 which identifiesthe height B). The scan mirrors 1522 and 1524 are each set at a distanceC (see 1518 in FIG. 15) from the ellipse center 1526. For theselocations to be at the focal points of the ellipse, the value of Cshould be defined as C=√{square root over (A²−B²)}.

Upstream from the reflector 1510 we insert a lens 1502, which focusesthe light emitted from the source 1500. As explained below, theellipsoidal reflector 1510 and lens 1502 can serve jointly as an afocallensing system. The shape and position of lens 1502 is chosen so thatthe focal point 1506 lies between the first scan mirror 1522 and thereflective surface of the ellipsoidal reflector 1510. Recall, that bydefinition, the focal point 1506 represents the location where the spotsize is at a minimum. The distance from 1506 to the location on theellipsoidal mirror whereupon the light source projects we denote by F2(1512). It is desirable that the light beam incident on the second scanmirror be collimated, in order that the output of the scan mirror 1522is also collimated. Hence, the optimum location of the focal point 1506as determined by the characteristics of the input beam 1500 and focusingelement 1502 can be made to conform to the requirement that the distance1512 is equal to the effective focal length F2 of the ellipsoidcorresponding to ellipse 1550 defined by the shape and curvature ofellipsoidal reflector 1510 at the point of reflection from 1510.

The angle α, 1516, is the offset tilt of the first scan mirror 1522.Note that as the tilt is varied on the 1^(st) scan mirror 1522, theangle of incidence (AOI) 1504 also varies. This does not constitute arequirement for using the system but offers additional flexibility topractitioners wishing to incorporate the system by decoupling thetrajectory of the input light from subsequently described geometricrequirements. We denote by the offset 1508 as the distance from thecenter 1526 of the ellipsoid projection 1550 to the center of theportion of the reflective surface of the ellipsoidal reflector 1510.

If a point source is positioned at one of the two foci of a prolatespherical ellipsoid, then light will all arrive at the second focuswithout aberration, and the total path length for all light rays will beequal. Therefore, in principle one can direct a light beam onto thefirst scan mirror 1522 from any angle and it will reflect onto thesecond scan mirror 1524 as long as that second scan mirror 1524 islocated at the second focus of the ellipsoid.

A more important factor influencing the beam input angle arises from thedesire to optimize the characteristics of the field covered by the scanpattern of the output beam. This can be appreciated by considering theoperation of an ideal two-mirror scanning system operating on opticalrays with no intervening optics. In such a system, the accumulation ofrays reflected for various tilt angles of the first mirror results in aset of reflected rays at various angles referred to here as a ray fan.It is desirable that all the rays in this fan lie in the same plane.This ray fan is then incident on a second mirror of sufficient extentthat all of the rays in the fan can be accommodated. When this secondmirror is scanned in a direction orthogonal to the first mirror, theresulting 2D output fan has the property that, when projected onto aplane perpendicular to the center ray, the 2D output fan forms a scanpattern in which the scan rows are linear and horizontal. The plane ofincidence of each member of the ray fan emanating from the first mirror,when incident on the second mirror, will then be rotated to an extentdetermined by the magnitude of the scan angle imparted by the X mirror.This results in a small pincushion distortion in the X direction only,which is visible in FIG. 16 as a deviation from the exact rectilinearpattern illustrated by the rectangular boundary. This distortion can bereadily accommodated by either adjusting the amplitude of the X mirrorscan for each Y position, or adjusting the laser pulse timing in theladar system.

Consider the ray fan from the first scan mirror 1522 as it encountersthe inside reflective surface of the ellipsoidal reflector 1510, fromwhich it reflects down onto the second scan mirror 1524. For an exampleembodiment, in order for the scanner to operate in the same desirablefashion as the ideal mirror pair previously described, after reflectionfrom the ellipsoidal reflector 1510, the fan of rays now converging ontothe center of the second scan mirror 1524 should all lie in the sameplane. This can occur only for the case where the intersection of thecenter ray of the fan lies directly above the second scan mirror 1524.

FIG. 17 illustrates a 3-dimensional view of the arrangement shown byFIG. 15, with a focus on the ray fan geometry. In FIG. 17, variouselements of FIG. 15 are again labeled (1500, 1502, 1522, 1524, 1510,1514), and the 3D ellipsoid is now drawn as a wire mesh, 1700. FIG. 17also adds the following labels: 1704 (for the image plane as presentedto the environmental scene), 1706 (for the fan beam from the second scanmirror 1524, 1708 (for the fan beam reflected by ellipsoidal reflector1510). FIG. 17 also shows the plane 1702 which encompasses the fan beam1708. It is useful to note that, in the case of an arbitrary geometry,the beam reflecting off the ellipsoidal reflector 1510 onto the secondscan mirror 1524 has a fan beam 1708 that is not planar.

For an example embodiment, making this fan beam 1708 planar places arequirement on the angle of reflection from the first scan mirror 1522.This angle is abbreviated the CPA (see 1514 in FIG. 15) for the coplanarangle. CPA is the angle subtended between the symmetry axis of theellipsoid and the intersection of the ellipsoid with the perpendicularline passing through the center of the second scan mirror 1524. CPA canbe calculated from the values of A and C which serve to define theellipsoid 1550, using the following expression (shown as 1528 in FIG.15):

${CPA} = {2{{\tan^{- 1}\left( \frac{A - C}{A + C} \right)}.}}$

To aid in ensuing design trades, we can add in an optional offset intilt angle, α, to the 1^(st) scan mirror 1522. We then obtain a modifiedformula for the CPA, shown as 1528 in FIG. 15 and re-created here forconvenience:

${CPA} = {{2\;{\tan^{- 1}\left( \frac{A - C}{A + C} \right)}} - {\frac{\alpha}{2}.}}$

Note that CPA 1528 is no longer mathematically exact (as is in the firstformula that did not include the addition of the optional offset tiltangle), but is rather an approximation sufficient for practical use.

Note that light does not interact with the ECR following reflection fromthe second scan mirror 1524, so an offset angle can be imposed on thesecond scan mirror 1524 to facilitate exit of the scanned volume withoutprejudice to performance.

The magnification between a collimated input 1500 and a collimated exitbeam (FIG. 15) is given by the ratio M=F2/F1. This is a consequence ofthe lens equation as applied to cascaded optical systems. In practice, apractitioner may want this ratio to be near unity, to keep both scanningmirrors 1522 and 1524 equal in size.

FIGS. 16 and 17 show how the CPA constraint can impact the constructionof useful ECR. FIG. 16 shows an example of the field resulting from a 24degree×20 degree (optical) scan of X and Y angles, respectively, when noattention is paid to ensuring the ECR is constructed and used with theCPA constraint. Note that FIG. 16 shows strong curvature in both Y and Xscan lines, making this pattern difficult to match with a rectilinearcoordinate system, especially problematic for co-boresighting cameraregistration with passive optics. FIG. 18 shows the same scan fieldoperated with the ECR constrained to operate according to 1528. Incontrast to FIG. 16, the scan rows (constant Y angle) are linear, andthe pincushion distortion along the X direction is equivalent to thatseen in the ideal (albeit non reimaged and therefor non-compact) systemwith no intervening optics. Note that in this pattern distortions in thesecond (vertical) scan angle mathematically vanish for alpha=0. Theresidual distortion in the first (horizontal) scan direction includes aminor over-scan similar to a 1D pincushion distortion, and is easilycompensated in post processing.

FIG. 19 shows the elegant form factor compaction we can obtain in anexample embodiment. The two scan mirrors, viewed from the side, aretightly packed with millimeter scales that are eminently feasible for anominal beam waist of order 100 um. Recall the direction of the firstmirror scan in this example embodiment is out of the plane, i.e. towardsthe viewer, while the second mirror scans within the plane containingthe image itself. For brevity and clarity labels are omitted in FIG. 19,but visible are the CPA angle, the scan mirror input and output rays,the input light beam source and input lens, and the ellipsoidalreflector. The 3D nature of this mirror is also visible in FIG. 19.

While the invention has been described above in relation to its exampleembodiments, various modifications may be made thereto that still fallwithin the invention's scope. Such modifications to the invention willbe recognizable upon review of the teachings herein. For example, whileLissajous scan patterns are disclosed as being a prime example of scanpatterns that can be enhanced via field inversion and induced periodicphase drift, it should be understood that spiral scan patterns can besimilarly enhanced. Such patterns are often implemented as dampenedLissajous patterns where the amplitude is slowly modulated.

What is claimed is:
 1. A scanner apparatus comprising: a first scannable mirror; a second scannable mirror; a lens that is positioned optically upstream from the first scannable mirror; and an ellipsoidal mirror that is positioned optically between the first scannable mirror and the second scannable mirror.
 2. The apparatus of claim 1 further comprising: a light source positioned optically upstream from the lens, wherein the light source is configured to transmit light through the lens onto the first scannable mirror, whereupon the first scannable mirror reflects the light toward the ellipsoidal mirror, and whereupon the ellipsoidal mirror reflects the light toward the second scannable mirror.
 3. The apparatus of claim 2 arranged as a ladar transmitter, the apparatus further comprising: a beam scanner controller configured to (1) scan the first scannable mirror along a first axis, and (2) scan the second scannable mirror along a second axis to define a scan pattern within a scan area; and a processor in cooperation with the light source and the beam scanner controller, the processor configured to intelligently select, via compressive sensing, a subset of range points for targeting with light from the light source via the first scannable mirror, the ellipsoidal mirror, and the second scannable mirror.
 4. The apparatus of claim 3 wherein the first and second scannable mirrors are positioned in a side-by-side arrangement.
 5. The apparatus of claim 4 wherein the first scannable mirror, the second scannable mirror, and the ellipsoidal mirror are positioned such that, with respect to an ellipsoid, (1) the first scannable mirror has a central region that is positioned at a first focus of the ellipsoid, (2) the second scannable mirror has a central region that is positioned at a second focus of the ellipsoid, and (3) the ellipsoidal mirror lies along the ellipsoid at a position that is optically between the first scannable mirror and the second scannable mirror.
 6. The apparatus of claim 5 wherein the ellipsoid has a major axis and an axis of symmetry along the major axis, and wherein the ellipsoidal mirror position is off the axis of symmetry.
 7. The apparatus of claim 1 wherein the ellipsoidal mirror exhibits rotational symmetry about its major axis.
 8. The apparatus of claim 7 wherein the ellipsoidal mirror has a prolate spheroidal shape.
 9. The apparatus of claim 1 wherein the first scannable mirror and the second scannable mirror comprise MEMS mirrors.
 10. The apparatus of claim 1 wherein the first scannable mirror and the second scannable mirror are of equal size.
 11. The apparatus of claim 1 further comprising: a beam scanner controller configured to (1) scan the first scannable mirror along a first axis, and (2) scan the second scannable mirror along a second axis to define a scan pattern within a scan area such that at least one of the first scannable mirror and the second scannable mirror scans at a sinusoidal frequency.
 12. The apparatus of claim 1 wherein the first and second scannable mirrors are positioned in a side-by-side arrangement.
 13. The apparatus of claim 1 further comprising: an optical field splitter/inverter positioned optically downstream from the first and second scannable mirrors to split and invert a scan area defined by the first and second scannable mirrors.
 14. A light steering method comprising: transmitting light toward a lens; the lens passing the transmitted light to a first scanning mirror; the first scanning mirror reflecting the transmitted light toward an ellipsoidal mirror; the ellipsoidal mirror reflecting the transmitted light toward a second scanning mirror; and the second scanning mirror reflecting the transmitted light.
 15. The method of claim 14 further comprising a processor intelligently selecting, via compressive sensing, a subset of range points for targeting by the ladar transmitter via the first and second scanning mirrors.
 16. The method of claim 15 wherein the first and second scanning mirrors are positioned in a side-by-side arrangement.
 17. The method of claim 16 wherein the first scanning mirror, the second scanning mirror, and the ellipsoidal mirror are positioned such that, with respect to an ellipsoid, (1) the first scanning mirror has a central region that is positioned at a first focus of the ellipsoid, (2) the second scanning mirror has a central region that is positioned at a second focus of the ellipsoid, and (3) the ellipsoidal mirror lies along the ellipsoid at a position that is optically between the first scanning mirror and the second scanning mirror.
 18. The method of claim 17 wherein the ellipsoid has a major axis and an axis of symmetry along the major axis, and wherein the ellipsoidal mirror position is off the axis of symmetry.
 19. The method of claim 14 wherein the ellipsoidal mirror exhibits rotational symmetry about its major axis.
 20. The method of claim 19 wherein the ellipsoidal mirror has a prolate spheroidal shape. 